I will explain about money transactions through PayPal. What I know as a developer of web systems with various payment methods.
From the client's side (end-user, user, payer):
Firstly, it is convenient that you do not need to enter information about the CC every time you pay via the Internet - once you have a PayPal account, tied the CC (or a bank, if you are in America) - and that's it! To pay, it is enough to log into PayPal, which the browser can do for you. A couple of clicks and you paid.
Secondly, there is no need to worry about the security of the payment - online payments via PayPal are redirected to secure pages of PayPal Payment Gateway, and they know a lot about this! Your CC data is stored only in PayPal, not in the database of some unknown online store.
From the side of the business (recipient of payments):
Possibility to divide cash flows and control them separately for different businesses (business areas). For example, if you have several online stores, then you can create your own PayPal account for each and control the balance / income / expense. Also useful for calculating taxes.
Your bank details are hidden from your customers. They don't know which bank is associated with your account, which country it is located in, etc. This is sometimes convenient when dealing with different political or national nuances between the parties. For example, you can make a deal with an Iranian client, being an Israeli citizen :-)
Well, there are many more nuances, but in general, direct bank transfers are used more often when transferring significant amounts in order not to pay 3% to PayPal.
P.S. SWIFT is one of the many ways to transfer money. Direct transfer requires IBAN - international bank account number
No, not required. Foreigners will be able to transfer money to your bank account if you provide them with your account details (just remember that a 20-digit account number and a 16-digit card number are not the same thing). Fortunately, SWIFT still works in Russia. Just in case, I recommend that you check with your bank before that which details you need to specify in the payment order to the sender of the money.